POLYA'S FOUR STEP PROBLEM SOLVING PROCESS ..., Assignments of Reasoning

Download POLYA'S FOUR STEP PROBLEM SOLVING PROCESS ... and more Assignments Reasoning in PDF only on Docsity! §1.1 KEY IDEAS POLYA’S FOUR STEP PROBLEM SOLVING PROCESS Understand Devise a Plan Carry out Plan Look Back PROBLEM SOLVING STRATEGIES (exmples) Making a Drawing Guessing and Checking Making a Table Using a Model Working Backwards §1.2 KEY IDEAS Patterns in Nature / Number Patterns Pascal’s Triangle Arithmetic Sequences Examples D & E Common Differences Geometric Sequences Example F Common Ratio Triangular Numbers Example G Finite Differences Examples H & I §2.1 KEY IDEAS, page 1 of 2 Set (Describe Set in Words) Set Elements (List Elements in Set) Venn Diagrams Disjoint Sets Empty Sets Subset Proper Subset Not a Subset §2.1 KEY IDEAS, page 2 of 2 Equal Sets, Not-Equal Sets 1:1 Correspondence, Equivalent Sets Finite Sets, Infinite Sets SET OPERATIONS Intersection (and) Union (or) Complement (not A, ~A, A’) Universal Set Math 211 Sets Practice Worksheet 1. Shade the region of the Venn diagram indicated by the following sets. (i) BA C (ii) BA C Shade: (A’ B)  C (A  B)’  C (iii) BA C (iv) BA C Shade: A  (C’  B) (A  B’)  C (v) BA C (vi) BA C Shade: A’  (C’  B) (A  B’)’  C §2.2 KEY IDEAS, page 1 of 2 FUNCTIONS What is a function? Function Domain Function Range Function Examples and Non-Examples (Example C) RECTANGULAR COORDINATES Axes, Coordinates, Cartesian Coordinate System LINEAR FUNCTIONS AND SLOPE Slope §2.2 KEY IDEAS, page 2 of 2 Y-Intercept Rate (Examples E, F) Linear Equations: Slope Intercept NONLINEAR GRAPHS Continuous Graph / Example H §2.3 Deductive Reasoning and Conditional Statement Venn Diagram Guide Conditional Statement: If P then Q Q P Universe Invalid Argument: Inverse Statement: If not P then not Q Q P Universe Invalid Argument: Converse Statement: If Q then P Q P Universe Valid Argument: Contrapositive Statement: If not Q then not P Q P Universe §3.1 KEY IDEAS, page 1 of 2 Grouping Number Bases Base Ten Numeration System Digits Expanded Form of a Number Egyptian Numerals §3.1 KEY IDEAS, page 2 of 2 Babylonian Numbers Mayan Numbers §3.2 KEY IDEAS, page 1 of 2 Sums and Addends Algorithm Partial Sums (Example C) Left to Right Addition NUMBER PROPERTIES / ADDITION OF WHOLE NUMBERS Closure / Not Closed Identity Associative §3.3 KEY IDEAS, page 2 of 2 Associative Distributive over Addition §3.4 KEY IDEAS, page 1 of 2 MODELS FOR DIVISION Measurement Sharing Rectangular Array Division Theorem EXPONENTS bn, b any number, n any whole number, b, n not both zero an  am, a any number, n, m any whole numbers except a, n, m = 0 an  am, a any number, n, m any whole numbers except a, n, m = 0 §3.4 KEY IDEAS, page 2 of 2 Order of Operations Equal Quotients Estimation of Quotients Rounding Compatible Numbers Front End Estimation §4.2 KEY IDEAS, page 1 of 2 What is a common multiple? What is a common factor? Prime Factorization—Example B Fundamental Theorem of Arithmetic PRIME FACTORIZATION Factor Trees Greatest Common Factor §4.2 KEY IDEAS, page 2 of 2 Least Common Multiple Relationship between GCF and LCM §5.1 KEY IDEAS, page 1 of 2 Positive and Negative Integers and their Uses MODELS FOR INTEGER OPERATIONS Addition Rules of Signs for Addition Subtraction Multiplication Rules of Signs for Multiplication Division Factor Game Board 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Advanced Factor Game Board 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 Math 211 Skills Test Practice No calculators should be used For each number pair, determine a) the prime factorization b) the GCF of the two numbers and c) the LCM of the two numbers A B A B A B 74529 30030 12100 21450 14176 125125 A B A B A B 36504 72930 15300 260100 2475 3510